Question

Write an inequality using absolute value if the answer is given double inequality

-2 is less than x and less than 4

Answer 1

|x-1|<3

Explanation:

Answer 2

`|x-1|<3`

Explanation:

You are given

`-2<x<4`

Note that

`(-2+4)/(2)=(2)/(2)=1,`

so, first, subtract 1 from this double inequality:

`-2-1<x-1<4-1\\ \\-3<x-1<3`

Now, rewrite it using absolute value:

`|x-1|<3`

Meaning: point x is less than 3 units away from point 1.